This invention is concerned with the field of electronic circuits, timing devices and clocks, and more particularly, it is related to the field of such devices having superconducting or Josephson junctions as circuit elements.
The use of Josephson junctions as electronic circuit elements only became possible after 1962 when the Josephson effect was discovered. At that time the only known superconducting materials had such low critical temperatures (i.e., temperatures below which the material becomes superconducting) that any circuit using Josephson junction elements required a source of liquid helium to maintain the low temperature required. Since that time the improvements in low-temperature technology, and also the discovery of high T.sub.c superconducting materials, have made these limitations less serious and increased the potential practical importance of electronic circuits designed with Josephson junction elements.
Josephson junctions are highly nonlinear and unusual circuit elements, and can be used to design circuits having many interesting and improved properties. The primary advantages of these junctions are their low power requirements and high operating speeds compared with conventional, nonlinear circuit elements. For the convenience of the reader, we briefly summarize some of the features and characteristics of Josephson junctions that were known to persons skilled in the relevant art prior to the present invention.
A Josephson junction is a junction between two superconducting materials that are closely spaced, forming electrodes in weak electrical contact. These junctions may be of several types, e.g., tunnel junctions, weak links, point contacts, bridges, etc. The essential requirement is that the superconductors on either side of the junction are coupled to each other.
The description of the electrical properties of the superconductors on each side of the junction is best cast in terms of the order parameters for these two materials, .psi..sub.1, .psi..sub.2. This quantity, first introduced in the phenomenological theory of Ginzburg and Landau [V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz. (Soviet Physics--JETP, Vol. 20, p. 1064 (1950)] is a complex-valued function of time and position in a superconducting material, and it satisfies a Schrodinger-like differential equation. It may be regarded as the average wave function for the carriers of supercurrent. (In the microscopic theory of Bardeen, Cooper and Schrieffer [J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. Vol. 108, p. 1175 (1957)], the order parameter is the average wave function of the so-called "Cooper pairs" which carry the electrical current.) Since .PSI. is complex-valued, it may be written as: EQU .psi.(r, t)=.vertline..psi.(r, t).vertline.e.sup.i.chi.(r,t). (1)
The square of the absolute value, .vertline..psi..vertline..sup.2 is the density of supercurrent carriers as a function of position and time. The phase of the order parameter, .chi.(r,t), is related to the flow of current within the material.
The superconducting materials on either side of the junction each have their characteristic order parameters and phases, .chi..sub.1 and .chi..sub.2. The electrical description of the junction itself is best described in terms of the difference between these two phases: EQU .phi.=.chi..sub.1 -.chi..sub.2, (2)
where .chi..sub.1 and .chi..sub.2 are evaluated at the interface between the superconducting material and the junction. The quantity .phi., called the "Josephson phase," or simply phase of the junction, is a function of time which determines the supercurrent flow through the junction and the voltage across the junction. These quantities are related by the two Josephson equations: EQU I.sub.s =I.sub.c sin.phi., (3) EQU .phi.=d.phi./dt=2e/n.times.V, (4)
where I.sub.s is the junction supercurrent, V is the voltage difference across the junction, e is the electronic charge and n is Planck's constant divided by 2.pi.. The quantity I.sub.c is called the critical current and represents the maximum value of the supercurrent I.sub.s. The critical current depends on the structure of the Josephson junction, and other variables. For simplicity, we will ignore these latter effects in the following discussion.
Equations 3 and 4 define the Josephson effect. Equation 3 shows that the junction supercurrent is a periodic function of the phase .phi. with period 2.pi., and can take any value from 0 to I.sub.c. At a given value of .phi., constant in time, since .phi.=0, Equation 4 indicates that V=0 so that this steady supercurrent flows with no voltage drop across the junction. This is known as the "dc Josephson effect."
If a dc voltage V is applied across the junction, Equation 4 shows that an alternating current will be produced in the junction, given by: EQU I.sub.s =I.sub.c sin(.phi..sub.0 +2e/n.times.Vt), (5)
where .phi..sub.0 is a constant of integration. The frequency of this alternating current is given by: EQU f=2e/h.times.V. (6)
This alternating current is called the "ac Josephson effect." The ratio between the oscillation frequency and applied voltage is 483.6 MHz/.mu.V.
In addition to the supercurrent flow through the junction, there can be other currents flowing by ordinary mechanisms. These must be considered in describing completely the electrical behavior of Josephson junction in circuits. At any finite temperature, there is always some normal current flow, given by I.sub.N, for any nonvanishing voltage V. These quantities are not necessarily proportional. However, when the temperature is only slightly below the critical temperature, or when the voltage is sufficiently high, we can write: EQU V=R.sub.N I.sub.N, (7)
where R.sub.N is the normal resistance of the junction, and its reciprocal, G.sub.N, is the normal junction conductance.
Furthermore, for any given capacitance of the junction C, there is a flow of displacement current through the junction when the voltage varies with time, given by: EQU I.sub.D =CV=C.times.dV/dt. (8)
Although the displacement current does not constitute any actual flow of electrical charges through the junction, it must be taken into consideration in describing the junction electrically. Therefore, the total current is given by: EQU I=I.sub.S +I.sub.N +I.sub.D. (9)
(We are neglecting complications in this simple description, such as thermal and noise fluctuations of the current.) This simple description, known as the resistively shunted junction (RSJ) model, is illustrated in FIG. 2. The curved line through the resistor symbol indicates the fact that the normal conductance is generally not constant but depends on the voltage V.
From the foregoing considerations, it is clear that a Josephson junction cannot be simply described in a circuit by a graph of voltage versus current, unlike most other nonlinear circuit elements. Clearly, a dc input signal can generate a time-dependent response in the junction. Nevertheless, we can use the RSJ model to construct an I-V curve that approximately describes the salient features of Josephson junctions and is sufficient for purposes of understanding the present invention. The character of this curve will depend on the parameters of the junction, and in particular, on the amount of damping. The damping of the junction is described by the parameter .beta.: EQU .beta.=2e/n.times.I.sub.C R.sub.N.sup.2 C. (10)
Junctions with .beta.&lt;&lt;1 are said to have high damping, and .beta.&gt;&gt;1 corresponds to low damping.
We can use the RSJ model to construct an I-V curve for the total junction current as a function of the time-averaged voltage. Such a curve is shown in FIG. 3 for the case of high damping (curve a) and low damping (curve b), assuming a constant normal conductance. Curve c is a more realistic representation that takes into account the variation of conductance with voltage.
This curve has a break or "knee" at approximately V.sub.g, the "gap voltage." This reflects the fact that when the average voltage across the junction exceeds the voltage required to break apart a Cooper pair and permit conduction by ordinary electron mechanisms, the effective conductance substantially increases.
From FIG. 3, it is apparent that if a current source drives a small current through the junction, no voltage difference will be developed across the junction. This condition remains true as the current is gradually increased, as shown by the arrow, until the current reaches its maximum value, I.sub.c. In this I-V regime, the junction is said to be in the "S-state," or stationary state.
When the current is driven over the limiting I.sub.c value it can no longer be carried solely by the supercurrent carriers, and a voltage develops across the junction. The condition of the junction then switches over to the appropriate curve on the plot of FIG. 3 as shown by the dashed line with arrows. The junction voltage shown in this plot is the time-averaged value; the actual voltage has an additional alternating component which varies with the average voltage itself. As the current gradually increases the I-V curves in FIG. 3 approach the straight-line plot of an ohmic junction. In the nonvanishing-voltage portion of the I-V curve, the junction is said to be in the "R-state," or resistance state.
As the current is again decreased gradually, the average voltage follows the curve back to the ordinate as shown by the arrow in FIG. 3. This voltage vanishes when the current is decreased to the "return current" value, I.sub.R. Below this value the junction switches back to the S-state (provided that the amplitudes of oscillations in the voltage are not too large). It is clear from the figure that when the junction damping is small, I.sub.R can be very small compared to I.sub.c. Under these conditions, the S-R transition exhibits a large hysteresis. For a highly damped junction the hysteresis is negligible.
Furthermore, although the RSJ model as discussed here describes the electrical properties of the junction itself, clearly from FIG. 2 we can adjust the model parameters by connecting a capacitance or resistance in shunt with the junction and using the model to describe the overall circuit as an "effective junction." Therefore, one can connect a resistance in shunt with a Josephson junction to produce an effective junction that is highly damped. Similarly, one could connect a capacitance in shunt with the junction to lower the damping.
FIG. 4 shows schematically the oscillations in the actual junction voltage as the above cycle is carried out. The upper graph is a plot of the driving current as a function of time. The lower graph shows the corresponding voltage across the junction. Initially, the junction is in the S-state, and at t=0, the current increases through the critical value I.sub.c and then remains constant at a value slightly greater than I.sub.c. This causes the junction to switch to the R-state, and the voltage rises to a value on the R-branch of the I-V curve. The fluctuations in the voltage during this increase are indicated on the graph. It is assumed that the junction is not heavily damped so that these acfluctuations are not negligible. Assuming also that the average voltage as a function of current is described by curve (c) of FIG. 3, the voltage rises to a value approximately V.sub.g.
At time t' the driving current decreases to 0, returning the junction to the S-state. The average voltage then decreases as shown in the lower graph of FIG. 4. The actual voltage decays with a series of "plasma oscillations." These oscillations are at the natural frequency of the junction, called the plasma frequency, arising from the coupling of the junction capacitance and the effective inductance reflected by the Josephson equations (3), (4), which state that a time-dependent current gives rise to a junction voltage. However, these oscillations are not generally sinusoidal, and indeed they are markedly nonsinusoidal as the mean voltage approaches 0. At higher mean voltages, on the other hand, the voltage oscillations are nearly sinusoidal.
The foregoing description shows that Josephson junctions may be used as switches in logic circuits, and indeed they are useful as logic gates in comparison with corresponding semiconductor elements. Silicon and gallium arsenide logic gates generally require at least two orders of magnitude more switching energy than Josephson logic gates, and switching times can be made at least an order of magnitude faster by using Josephson junction technology. The delay times on the voltage graph in FIG. 4 can be of the order of several picoseconds. The high speed and low power requirements of Josephson logic elements make them attractive candidates for use in computer circuits and information processing devices.
An example of a useful Josephson logic circuit is the two-junction interferometer, which is a circuit having two Josephson junctions in a superconducting loop. This circuit is a dc type of superconducting quantum interference device (SQUID). FIG. 5 is a schematic diagram of such a circuit. Two Josephson junctions, labeled "1" and "2," are placed in a closed circuit of otherwise superconducting material. A nearby conductor carries a control current I.sub.con, which generates an externally controlled magnetic flux .PHI..sub.ex threading the interior of the superconducting circuit. The two junctions are driven by a gate current I.sub.g that is fed to the circuit between the junctions, as shown in the figure. For simplicity, we assume that the two junctions are identical, with phases .phi..sub.1 and .phi..sub.2, and that the circuit is symmetrical with respect to the two branches. We also assume that the junctions are highly damped and their critical currents are equal, I.sub.c.
If the superconducting circuit were unbroken, the total magnetic flux .PHI. through the interior of the loop would be quantized in units of the basic quantum of flux: EQU .PHI..sub.o =h/2e=2.07.times.10.sup.-15 Webers. (11)
Because the loop is interrupted by the junctions, the total flux in the loop can deviate from integer multiples of this value. (We assume that the flux in the junctions themselves is small compared to .PHI..sub.o.) When one of these junctions switches to the R-state, the superconducting loop is broken, and one or more flux quanta may enter or leave the loop. Therefore, there are a multiplicity of stable states of the circuit where both junctions are in the S-state. These states are characterized by the number of flux quanta in the loop. This plurality of stable states enables this circuit to function as a digital logic device.
If the control current and total magnetic flux through the loop are initially 0, the gate current I.sub.g is split equally between the two junctions. These junctions will remain in the S-state as I.sub.g increases up to a maximum value, I.sub.gc, which in this case is 2I.sub.c. Since I.sub.1 and I.sub.2 are equal, the total magnetic flux through the loop produced by these currents is 0.
Now we assume that the number of quanta in the loop is 0 and the junctions are in their S-states, but that the control current I.sub.con is given a finite value, flowing to the right in FIG. 5. This control current will cause a magnetic flux .PHI..sub.ex to thread the loop. In order to try to maintain the number of quanta in the loop equal to 0, a compensating current I.sub.circ is induced in the loop in the counterclockwise direction. Therefore, I.sub.1 is greater than I.sub.2. Choosing sign conventions according to the arrow directions in FIG. 5, EQU I.sub.circ =1/2.times.(I.sub.1 -I.sub.2). (12)
The gate current may be increased from 0 up to its maximum value at which I.sub.1 reaches the critical current: EQU I.sub.gc =2(I.sub.c -I.sub.circ). (13)
Thus, the maximum value of the gate current is decreased by turning on the control current.
Quantitatively, the two-junction interferometer is described by the basic equation: EQU .phi..sub.1 -.phi..sub.2 =2.pi..times..PHI./.PHI..sub.0, (14)
which relates the junction phases to the total flux through the loop. This total flux is given by: EQU .PHI.=.PHI..sub.ex -LI.sub.circ, (15)
where L is the self-inductance of the loop. When the junctions are in the S-state, EQU I.sub.1 =I.sub.c sin .phi..sub.1, (16) EQU I.sub.2 =I.sub.c sin .phi..sub.2. (17)
These equations can be solved to determine the maximum gate current I.sub.g and total flux .PHI. as functions of I.sub.1 (or I.sub.2) and .PHI..sub.ex (or I.sub.con). As discussed above, these solutions have a plurality of branches, each branch corresponding to the integer multiple of .PHI..sub.0 closest to .PHI.. FIG. 6 comprises graphs of the maximum value of I.sub.g for both junctions to remain in the S-state, and the corresponding values of I.sub.1 and I.sub.2, as functions of the externally imposed flux through the loop, .PHI..sub.ex. The solutions are labeled by the branch number n, which is the approximate number of flux quanta through the loop in the branch, i.e., n=0 corresponds to 0 total flux, n=1 corresponds to a total flux .PHI..sub.0, etc. This is shown in FIG. 7, which is a plot of total flux through the superconducting loop as a function of the externally applied magnetic flux generated by the control current I.sub.con.
FIG. 6 shows that there are ranges of values of .PHI..sub.ex for which the superconducting loops have two stable states in which both junctions are in S-states, namely the regions where .PHI..sub.ex is nearly an odd multiple of 1/2.PHI..sub.0. FIG. 8 is a plot of the maximum gate current I.sub.gc as a function of .PHI..sub.ex for values of .PHI..sub.ex near 1/2.PHI..sub.0 ; i.e., FIG. 8 is an enlarged plot of the corresponding portion of the I.sub.gc graph in FIG. 6. Referring to this graph, for value of .PHI..sub.ex between .PHI.. and .PHI..sub.+, there are two stable states of the circuit, one corresponding to n=0 and the other corresponding to n=1. Since the maximum magnetic flux through the loop in this range is approximately .PHI..sub.0, this is called the "single flux quantum" (SFQ) regime.
From FIG. 8 it is clear that in order to switch the circuit from the n=0 to n=1 region and remain in the S-state for both junctions, the gate current must not be too high. In fact, the gate current must be less than I.sub.M (FIG. 8). For example, point A has a gate current I.sub.A &gt;I.sub.M. As the control current is increased, the loop will be driven into a R-state; a voltage will develop across both junctions.
Point B falls below the limiting gate current for both branches. Nevertheless, if the junctions are not sufficiently damped, increasing .PHI..sub.ex will drive the junctions into the R-state because of the ac fluctuations as the junction current reaches the critical value I.sub.c. In order to remain in the S-state the gate current must fall below some value I.sub.Q which depends on the damping parameter .beta.. For example, point C will be driven from the n=0 S-state to the n=1 S-state as the external flux .PHI..sub.ex increases past the value .PHI..sub.1. Note also that in order to return to the n=0 condition at this gate current, the external flux .PHI..sub.ex must decrease to the value .PHI..sub.2. Thus this circuit exhibits a kind of hysteresis in switching between the 0 and single quantum flux states. This should be distinguished from the hysteresis of underdamped junctions discussed previously.
Finally, we note that two-junction interferometers may be driven by current pulses as well as magnetic fluxes. If a gate current pulse is applied to the circuit at point D, the loop will again be driven from the n=0 to the n=1 condition, in the S-state.
The above description of a two-junction interferometer illustrates how it can be operated as a memory cell, and in particular, how a write operation would be carried out. A read operation would employ a similar process. This particular mode of operation would result in a destructive readout, but Josephson junction circuits have been designed for memory cells with nondestructive readout.
A variety of other logic circuits have been designed using Josephson junctions. An article by J. P. Hurrell, D. C. Pridmore-Brown and A. H. Silver, "Analog-to-Digital Conversion with Unlatched SQUID's," IEEE Transactions on Electron Devices. Vol. ED-27, No. 10, October 1980, pp. 1887-1896, discloses a high-speed A/D converter using bistable two-junction SQUID's. A Josephson junction flip-flop circuit is described in the paper by A. F. Hebard, S. S. Pei, L. N. Dunkleberger and T. A. Fulton, "A DC-Powered Josephson Flip-Flop," IEEE Transactions on Magnetics, Vol. MAG-15, No. 1, January 1979, pp. 408-411. D. A. Peterson, H. Ko and J. Van Duzer discuss a latching comparator in their paper "Dynamic Behavior of a Josephson Latching Comparator for use in a High-Speed Analog-to-Digital Converter," IEEE Transactions on Magnetics, Vol. MAG-23, No. 2, March 1987, pp. 891-894. A clipping circuit using a Josephson junction is disclosed in the paper by D. A. Peterson, D. Hebert and T. Van Duzer, "A Josephson Analog Limiter Circuit," IEEE Transactions on Magnetics. Vol. 25, No. 2, March 1989, pp. 818-821.
Finally, a two-junction SQUID flip-flop with transmission lines has been used to construct a clock, described in the paper by G. S. Lee, A. H. Silver and R. D. Sandell, "An On-Chip Superconducting Clock with Two Modes," IEEE Transactions on Magnetics, Vol. 25, No. 2, March 1989, pp. 834-836. The SQUID described in this paper operates at a frequency that depends on the total magnetic flux threading the SQUID. Therefore, the clock is sensitive to any accidental trapping of magnetic flux that may occur.